This document summarizes a lecture on memory in digital circuits: 1) The lecture discusses different types of memory circuits including basic latches, gated SR latches, D latches, and their functionality. 2) Timing diagrams are presented showing how a D latch stores input data on the rising edge of a clock signal. 3) The concept of critical path is introduced and used to determine the maximum clock frequency of a simple circuit. 4) Different units of time and frequency are defined, with conversions between seconds (s), Hertz (Hz), milliseconds (ms), microseconds (μs), etc. 5) A problem is presented analyzing the output sequence of a circuit with multiple flip

1. ECE 287 – Lecture 12
• Memory 1

2. Announcements
• Next Quiz on Wednesday
• Exam II – Nov 15th

7. Starter…
Draw a circuit for the following:
while (A+B > 10)
A--;

8. Memory
What is memory in a non technical context?
What are some key words about memory?
What happens in our brain?

10. Basic Latch
R
!Q
S
Q

11. Gated SR Latch
R
R`
Clk
S`
S
Q

12. D Latch
D
Clk
Q

13. D Latch
Q
D
clk

14. D Latch
0
1
2
3
4
5
6
7
8
9
10
clk
D
Q
What does Q look like assuming no delays through
gates?

15. Critical Path
a
b
ff
ff
clk
c
o
clk
Assume 1ns delay through all gates. Where’s the critical
path

16. Frequency
1s is related to 1Hz
Frequency = 1/time
How many things per second?
How fast can the circuit be clocked at?

17. Value
Symbol
Name
Hz
Term
s
s
second
1
1 Hz
10−1 s
ds
decisecond
10
10−2 s
cs
centisecond
100
10−3 s
ms
millisecond
1000
1 KHz
10−6 s
µs
microsecond
1000000
1 MHz
10−9 s
ns
nanosecond
1000000000
1 GHz
10−12 s
ps
picosecond
1000000000000 1 THz
10−15 s
fs
femtosecond
10−18 s
as
attosecond
10−21 s
zs
zeptosecond
10−24 s
ys
yoctosecond

18. Problem Set
1. What is the output of the following circuit for each clock
assuming the flip-flops are initialized as follows: ff0 = 1, ff1 = 0,
ff2 = 0, and ff3 = 0. Does the sequence ever end or repeat? What
might this be good for? What’s the critical path?
ff0
clk
ff1
ff2
ff3